algorithm - Finding the average intersection line for multiple planes -

i have planes in 3d space, in theory should intersect @ same line.

each plane calculated taking 3 measured points. there error in measurement of these points.

so in practice, planes not intersect @ same line.

how can "average" intersection line these planes?

i intersect each plane each other plane, , average lines. however, when 2 planes have same orientation, small error in measurements result in huge error in calculated intersection. magnifying measurement error when calculating average intersection way.

is there fairer way calculate common intersection line?

i think need not averaging algorithm detects outliers (i.e. bad intersections lines) , discards them.

one standard algorithm doing random sample consensus (ransac). able use have define kind of distance between lines, should possible in meaningful way.

another possibility find inlier (i.e. intersection lines) hough transform. in algorithm, whole parameter space of lines subdivided cells. calculated intersection line "votes" cell contain parameters of intersection line. parameter cell votes wins. 1 can refine result calculating average line lines voted winning cell.